Elliptic curve isogeny class 6400.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-6400.2-a
• Conductor: 6400.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Elliptic curves in class 6400.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 6400.2-a contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
6400.2-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 i - 173\) , \( -930 i - 728\bigr] \)
6400.2-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 i - 173\) , \( 930 i - 728\bigr] \)
6400.2-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -13\) , \( 34 i\bigr] \)
6400.2-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 240 i - 133\) , \( -246 i - 1680\bigr] \)
6400.2-a5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -240 i - 133\) , \( 246 i - 1680\bigr] \)
6400.2-a6	\( \bigl[0\) , \( 0\) , \( 0\) , \( 7\) , \( -6 i\bigr] \)
6400.2-a7	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -i\bigr] \)
6400.2-a8	\( \bigl[0\) , \( 0\) , \( 0\) , \( 107\) , \( -426 i\bigr] \)
6400.2-a9	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1920 i - 2773\) , \( 59450 i - 46368\bigr] \)
6400.2-a10	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1920 i - 2773\) , \( -59450 i - 46368\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 2 & 8 & 2 & 4 & 8 & 8 & 8 & 2 \\ 4 & 1 & 2 & 2 & 8 & 4 & 8 & 8 & 2 & 8 \\ 2 & 2 & 1 & 4 & 4 & 2 & 4 & 4 & 4 & 4 \\ 8 & 2 & 4 & 1 & 16 & 8 & 16 & 16 & 4 & 16 \\ 2 & 8 & 4 & 16 & 1 & 8 & 16 & 16 & 16 & 4 \\ 4 & 4 & 2 & 8 & 8 & 1 & 2 & 2 & 8 & 8 \\ 8 & 8 & 4 & 16 & 16 & 2 & 1 & 4 & 16 & 16 \\ 8 & 8 & 4 & 16 & 16 & 2 & 4 & 1 & 16 & 16 \\ 8 & 2 & 4 & 4 & 16 & 8 & 16 & 16 & 1 & 16 \\ 2 & 8 & 4 & 16 & 4 & 8 & 16 & 16 & 16 & 1 \end{array}\right)\)

Isogeny graph